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王秋宇 · 2022年01月02日

这题目的答案给的也太不容易辨别了吧。

  1. CFA I
  2. Quantitative

NO.PZ2017092702000006

问题如下：

For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to:

选项：

A.

555.

B.

563.

C.

576.

解释：

A is correct.

The effective annual rate (EAR) is calculated as follows:

EAR = (1 + Periodic interest rate)m – 1   EAR = (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%.

Solving for N on a financial calculator results in (where FV is future value and PV is present value):

(1 + 0,030453）N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 years, which multiplied by 12 to convert to months results in 554.5, or ≈ 555 months.

看了答案后，我知道，题目中将年利率，换算成了按天计息的年度有效利率，然后算出年，再乘以12。 我把3%除以365。得出天利率0.0082%。(1+0.0082%)的30n次方等于4，把A和B代入等式后，得出3.9292和4.0312的结果。我就确定一下，此处比较应该和4比吧，是不是这么个比法，分别算两个值和4的差，前者约差0.0708，后者约差0.0312，后者小，所以选后者

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4 个答案

星星_品职助教 · 2022年05月10日

@milky

同学你好，已在你单独的提问中回复此题，相同的问题提问一次即可。

milky · 2022年05月10日

题目问大概需要多少个月，ear中的m用的是365天，为何不能用12个月来求ear

星星_品职助教 · 2022年04月23日

@Barry Liu

符号只代表方向。绝大部分情况下，PV和FV的方向都是相反的。

本题也可以PV为正，此时要把FV设成负，结果不变。

如果本题PV和FV同时为正或者同时为负，计算器会显示ERROR

星星_品职助教 · 2022年01月03日

同学你好，

答案并不是这么给出的。

答案解析的思路是先转化EAR=3.0453%，然后根据计算器得到N=46.21年，然后乘以12得到554.5个月。

此时计算器按键为：PV=-250000， I/Y=3.045，PMT=0，FV=1000000， CPT N=46.21（年），然后乘以12得到554.5月


Barry Liu · 2022年04月23日

这里为什么把PV设成负呢？计算器问题吗？

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NO.PZ2017092702000006 问题如下 For a lump sum investment of ¥250,000 investea stateannurate of 3% compounily, the number of months neeto grow the sum to ¥1,000,000 is closest to: A.555. B.563. C.576. A is correct. The effective annurate (EAR) is calculatefollows: E= (1 + Perioc interest rate)m – 1   E= (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financicalculator results in (where FV is future value anPV is present value): (1 + 0,030453）N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 years, whimultiplie12 to convert to months results in 554.5, or ≈ 555 months. 这题我EAR已经算出来是3.045，带入计算器知四求一不知道为什么算出来是46.21.

2023-06-02 16:31 1 · 回答

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NO.PZ2017092702000006问题如下 For a lump sum investment of ¥250,000 investea stateannurate of 3% compounily, the number of months neeto grow the sum to ¥1,000,000 is closest to: A.555. B.563.C.576. A is correct. The effective annurate (EAR) is calculatefollows: E= (1 + Perioc interest rate)m – 1   E= (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financicalculator results in (where FV is future value anPV is present value): (1 + 0,030453）N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 years, whimultiplie12 to convert to months results in 554.5, or ≈ 555 months. 为什么用 FVN/PV

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